Numerical control system for providing a constant rate of metal removal

ABSTRACT

A numerical control system for providing a constant rate of metal removal in terms of surface feet per unit time. The operative relationship between the rotational speed of a rotating workpiece (RPM), the effective radius in inches of the rotating workpiece (R) and the desired rate of metal removal in surface feet per minute (SFM) is defined as: The relationship is mechanized by a plurality of digital integrators which generate pulse frequency signals proportional to each side of this relationship. These pulse frequencies are then compared with the result of this comparison affecting the speed of the rotating workpiece so as to close the control loop and fully mechanize this relationship. In one embodiment, the pulse frequencies are compared by generating phase varying signals which are then phase compared. In another, a single phase varying signal is generated and phase compared with a constant phase signal. A number of alternative embodiments are disclosed for indicating the speed of the rotating workpiece including a novel digitizer which also provides a steady state signal indicative of workpiece rotational speed.

United States Patent Bakel et al.

- [54] NUMERICAL CONTROL SYSTEM FOR PROVIDING A CONSTANT RATE OF 1451May 23, 1972 Primary Examiner-Joseph F. Ruggiero Attorney-William S.Wolfe, Frank L. Neuhauser, Oscar B.

721 Inventors: Joseph F. Bakel, Lyndhurst; George L. [57-] ABSTRACTRogers Wayne-S5010, both of A numerical control system for providing aconstant rate of may metal removal in terms of surface feet per unittime. The [73] Amgnee' General Electric Com operative relationshipbetween the rotational speed of a rotat- [22] Filed: Dec. 12, 19,69 ingworkpiece (RPM),'the effective radius in inches of the rotatingworkpiece (R) and the desired rate of metal removal in surface esprminute SW) .1 fine! s l T '1 '1 52 us. Cl ..23s/1s1.11, 90/13 0,90/DIG. 27, f R =f SFMXI 1-9095 I 318/39, 318/569 I r [5 1 1 Int. Cl..G05b 19/18, B23q 5/22 The relationship is mechanized by a plurality ofdigital integra- 58 Field orseereh ...318/39.569,570, 572, 600,tors-which generate pulse frequency signals proportional to 318/60 0/ 3.1 235/ 151.1 1 each side of this relationship. These pulse frequenciesare then compared with the result of this comparison affecting the 5 m-Cited speed of the rotating workpiece so as to close the control loopand fully mechanize this relationship. In one embodiment, the UNITEDSTATES PATENTS pulse frequencies are compared by generating phasevarying h are then phase compared. In another, a single 2,600,988 6/1952Greene et a1. ..31s/39 F 2,809,333 10/1957 Wagner ..318/39 x Phase and 83,090,266 5/1963 Wagner 31 nstant phase signal. A number of alternativeembodiments 3.109.974 11/1963 Hallmark 315/571 x dimbwdf indicating.Peed wins 3,339,313 6/1968 Reynolds ..31s/39 indudilfl a digitize whichPmvid a 34 3549, 12/1968 Emerson et a! 1 8/39 state signal indicative ofworkpiece rotational speed. 3,548,172 12/1970 Centner et al. 35/151.1 147 Claims, 7 Drawing Figures SPINDLE SPEED VARIABLE ADV PHASE COUNTER.

RET

SPINDLE SERVO DRIVE R (INCHES) "x" POS MOTIO1IEIOPULSES "x" AXIS sER'vo.

Patented May 23, 1972 3,665,170

4 Sheets-Sheet 1 ARITHMETIC UNIT SPINDLE SERVO 5; DRIV l'l lll l"INTERATION RATE * MONITOR INTEGRAND OUTPUT PULSES INVENTORS JOSEPH F.BAKEL GEORGE 1.. ROGERS THEIR ATTORNEY UFFER Patented May 23, 19723,665,170

4 Sheets-$heet 2 T" T F VARIABLE PHASE 66 I I COZL I E R COPRAT SPINDLEI SPEED D/A T RTER 84 FM VARIABLE S ADV PHASE SPINDLE m COUNTER SERVO 5O62 MOTION PULSES I. To

X AXIS SERVO I FREQUENCY DIVIDER D I$I%%R F 66 SPINDLE 6O W420 VARIABLESFM ADVPHASE :j

COUNTER R (INCHES) 72 I n JOSEPH X P08 X NEG BY GEORGE E. [ROGERS MOTONPULSES I TO W M "X" AXIS SERVO THEIR ATTORNEY 4 Sheets-$heet 4 PatentedMay 23, 1972 BAKEL ROGERS 7am WM THEIR ATTORNEY JOSEPH GEORGE E) KEEEEOQH NUMERICAL CONTROL SYSTEM FOR PROVIDING A CONSTANT RATE OF METALREMOVAL BACKGROUND OF THE INVENTION the advent, however, of solid stateelectronic devices there has been substantial improvement in both thecomplexity and speed of numerical control systems. As a result of thisadvance in technology, the advances in the numerical control systemshave included not only increased speed and accuracy but also thecapability of performing and controlling an ever increasing number offunctions.

One of the latest developments in numerical control systems is referredto broadly under the term adaptive control." Under this phase ofnumerical control development, the operation of the controlled machinehas been controlled by sensing various conditions during the actualmetal cutting operation and modifying the operation of the controlsystem accordingly. Thus, it is now known to sense torque, tooltemperature, and other variables in the system and to modify theoperation of the system accordingly.

In programming prior art numerical control systems, one of many factorsto be taken into account, particularly for a controlled lathe, has beenreferred to as surface feet per minute metal removal rate. That is, thespeed of the rotating workpiece has been synchronized with the rate atwhich the cutting tool advances so as to provide substantially aconstant rate of metal removal when measured in terms of the surfacefeet per unit time. In order to maintain this characteristic, it hasbeen necessary in prior art systems to continually change theinformationfed into the control system so as to reflect a change in the radius ofthe rotating workpiece as the cutting tool advances toward the center ofthe rotating workpiece. Generally, this is accomplished by driving thecutting tool toward the center of the workpiece at a constant rate andin creasing the speed of the rotating workpiece as the effective radiusof the workpiece decreases. In most machine tools, the speed is notincreased on a continuous basis but rather the programmer changes thespeed incrementally as the effective radius decreases so as toapproximate a constant surface feet per unit time metal removal rate. Itwill be apparent from the foregoing, that the accuracy (and thereforethe condition of the cut) varies widely depending upon the actualprogram used to control the speed of the rotating workpiece.

In the so-called adaptive control systems, the speed of the rotatingworkpiece and/or the speed of the cutting tool may be varied adaptivelyas a function of the actual cutting conditions. That is, when aprogrammer selects the optimum rate of machine tool performance, heordinarily does so from standard factors relating to the particular typeof tool used and the particular type of metal being operated on. Thesefactors are, at best, approximations of the actual conditions in anygiven operation and are for the most part essentially conservative. Anadaptive control system, on the other hand, takes into account theactual conditions extant at the time a particular operation takes place.As a result of sensing these actual conditions, the performance of themachine will be varied.

It will be appreciated from the foregoing that an adaptive controlsystem poses particular problems as regards constant surface feet perminute metal removal. It is no longer feasible to simply program changesin the speed of the rotating workpiece so as to take into account thedesired surface feet per minute removal rate since the speed of thespindle and/or the cutting tool may be varied as a result of theadaptive control function.

Finally, in a control system which has significant control over thecontinuous speed of the rotating workpiece, it may be necessary toprovide a steady state indication of the actual speed of the rotatingworkpiece. This presents some problems in conventional systems since thespeed of the rotating workpiece is generally represented by either ananalog signal as from a conventional tachometer, or, alternatively, byway of a pulse frequency signal from a digital encoder. Therefore, itmay be necessary in certain types of control systems to digitize theactual spindle speed so as to provide a steady state digital signalindicative of the actual speed of the rotating workpiece.

SUMMARYOFTI-IE INVENTION Accordingly, it is an object of the presentinvention to provide a novel numerical control system.

It is a further object of the present invention to provide a novelnumerical control system having the capability of controlling the speedof a rotating workpiece on a continuous ba- SIS.

It is a still further object of the present invention to provide such anovel numerical control system which continuously maintains a desiredsurface feet per unit time rate of metal removal from a rotatingworkpiece.

It is a still further object of the present invention to provide a noveldigitizer which provides a steady state digital signal indicative of apulse frequency signal applied to its input.

It is a still further object of the present invention to provide such anovel digitizer which also provides an output frequency proportional tothe input pulse frequency.

Briefly stated, the present invention accomplishes these and otherobjects by mechanizing the mathematical relationship between theeffective radius of the rotating workpiece, the rate at which theworkpiece is rotating, and the desired surface feet per unit time rateof metal removal. This is accomplished by generating a first digitalsignal which is proportional to the desired surface feet per unit timeand equating that signal with a second digital signal proportional tothe product of the effective radius of the rotating workpiece and thespeed of the rotating workpiece. These two signals are compared and as aresult of this comparison the speed of the rotating workpiece is variedso as to maintain the desired surface feet per unit of time of metalremoval.

BRIEF DESCRIPTION OF THE DRAWINGS While the specification concludes withclaims particularly pointing out and distinctly claiming the subjectmatter which is regarded as the invention, an illustration of severalparticular embodiments can be seen by referring to the specification inconnection with the accompanying drawings in which:

FIG. 1 is a block diagram of a typical numerical control system forcontrolling an illustrative machine tool;

FIG. 2 is an illustration of the operation of such a machine toolshowing in detail the rotating workpiece and the cutting tool;

FIG. 3 is the operational symbol for an integrator as used in FIGS. 4-7;

FIG. 4 is a block diagram illustrating an embodiment of the presentinvention;

FIG. 5 is a block diagram of a further embodiment of the presentinvention;

FIG. 6 is a block diagram of a still further embodiment of thepresentinvention; and

FIG. 7 is a block diagram of a still further embodiment of the presentinvention.

DESCRIPTION OF THE PREFERRED EMBODIMENT Before turning specifically tothe subject matter comprising the preferred embodiment of the presentinvention, it will be necessary briefly to describe a particular type ofnumerical control for machine tools. Turning then to FIG. 1, there isshown a conventional engine lathe which includes a workpiece 12 mountedbetween a headstock 14 and a tailstock 16. The workpiece 12 is mountedin a chuck 18 which is rotated by spindle drive motor 20 so as to rotatethe workpiece 12. The spindle drive motor 20 is connected to a gear box22 so as to provide a plurality of gear ranges within which variouscutting speeds can be achieved.

The workpiece 12 is operated on by a cutting tool 24. The cutting tool24 is mounted in a tool post 26 which is in turn mounted on a lead screw28. Lead screw 28 is driven by an X" axis drive motor 30. As the X drivemotor 30 rotates, the cutting tool 24 will be moved in the appropriatedirection relative to the workpiece 12.

In order to move the cutting tool 24 parallel to the rotating axis ofthe workpiece 12, the cutting tool and its associated drive are mountedon a second lead screw-32. Lead screw 32 is coupled to the Y axis drivemotor 34. In this fashion, rotation of the Y" axis drive motor 34results in moving the cutting tool 24 parallel to the rotating axis ofthe workpiece 12.

The machine tool described above will be recognized by those skilled inthe art as a conventional engine lathe. As such, it is described hereinonly as representative of a variety of possible machine toolconfigurations which can utilize the present invention and is in no wayto be construed as a limitation upon the present invention or itspossible uses. Thus, the above description is exemplary only.

The remainder of FIG. 1 relates to a block diagram of a known type ofnumerical control system which is adapted to control the operation ofthe machine tool exemplified by the lathe 10. A control system of thistype is described in detail in co-pending U.S. patent application Ser.No. 709,242, filed Feb. 29, 1968 by James P. Corbett et' al. andassigned to the assignee of the present invention. The numerical controlsystem disclosed in the above-cited US. patent application is to beconsidered only one way of carrying out the present invention since anytype of numerical control system could be arranged so as to operate inaccordance with the principles of this invention. Therefore, the presentinvention is not to be considered limited to a control system of thatparticular type.

Briefly, the control system described in the above-cited US. patentapplication includes a delay line 36 for storage of the operationaldata. The delay line 36 receives its data from a write amplifier 38 andfeeds its output data through a read amplifier 40. The output of theread amplifier 40 forms one input to an arithmetic unit 42. After thenecessary manipulations in the arithmetic unit 42, the data is returnedto the delay line 36 by way of the write amplifier 38. Thus, thecombination of delay line 36, amplifiers 38, 40, and arithmetic unit42'forms a circulating data storage loop.

In such a numerical control system, data may be provided by some wellknown type of data input means such as a tape reader 44. The data fordescribing the desired operation of the machine tool 10 is coded intosome type of tape such as punched or magnetic tape. The tape reader 44is connected to an additional input to the arithmetic unit 42. It willbe apparent that entering data from the tape reader 44 into thearithmetic unit 42 allows that data to be ultimately placed on the delayline 36 and, therefore, to be stored within the recirculating datastorage loop.

The basic function of the arithmetic unit 42 is to carry out the variousarithmetical computations that are required in a numerical controlsystem of this type. After these computations take. place, the data isgenerally returned to the delay line 36. However, it will also beapparent that certain control functions result from the computations inthe arithmetic unit. In particular, the controlled axes of the machinetool 10 must be moved in accordance with the data provided from the datainput means 44. Thus, the arithmetic unit 42 has a number of additionaloutputs which feed pulses or other signals to the appropriate devicesfor controlling the operation of the machine tool 10. Thus, for example,there is provided an X" axis servo drive 46 and a Y axis servo drive 48which receive instructions from the arithmetic unit 42 and control therotation of the X" axis drive motor 30 and the Y axis drive motor 34,respectively.

In addition to the drive for the controlled machine axes, it is alsonecessary to provide a spindle servo drive 50 which controls the speedand operation of the spindle drive motor 20.

Briefly, it can be seen that the numerical control system of FIG. 1carries out certain arithmetic computations on the data received fromthe data input means 44. As a result of these computations, the variousaxes and functions of the controlled machine tool 10 take place underthe fully automatic control of the numerical control system. Suchnumerical control systems are, of course, well known in the art and formno part of the present invention per se. Rather, the present inventiondeals with a particular aspect of an improved type of numerical controlsystem as will be described in detail hereinafter.

As pointed out hereinbefore, a primary object of the present inventionis to provide automatically for the control of a nu merical controlledmachine tool so as to provide a constant rate of metal removal in termsof constant surface feet per minute. FIG. 2 is a symbolic representationof the rotating workpiece 12, the cutting tool 24 and the tool post 26.This figure will be referred to briefly for the purposes of explainingthe desired characteristics of constant surface feet per minute metalremoval. During the operation of the machine tool 10 of FIG. 1, theworkpiece 12 may be rotating, for example, in the direction illustratedby the arrow 52 in FIG. 2. Similarly, the tool post 26 and cutting tool24 will'be advancing toward the rotating workpiece 12 in the directionindicated by the arrow 54. If the speed of the rotating workpiece 12 isheld constant as the cutting tool 24 moves into the workpiece 12 in thedirection shown by arrow 54, it will be apparent that the surface rateof metal removed from the workpiece 12 will vary. This is due to thefact that as the cutting tool 54 removes metal from the workpiece 12,the effective radius of the workpiece I 12 decreases.

That is, as the effective radius of the workpiece 12 decreases it willbe apparent that the surface feet per minute of metal removed from theworkpiece 12 goes through a corresponding decrease. Mathematically, therelationship between surface feet per minute and the rotational speed ofthe workpiece can be expressed as follows (assuming that the cuttingtool 24 moves toward the center of the workpiece at a constant speed):

(1) Surface Feet Per Minute (SFM) Circumference of Rotating Workpiece(in Feet) Rotational Speed of Rotating Workpiece in (RPM).

If the effective radius R of the workpiece l2 (i.e., at the cuttingtool) is expressed in inches:

As was pointed out briefly hereinbefore, one of the primary objects ofthe present invention is to provide a novel numerical control systemincluding a novel control system for providing constant surface, feetper minute. The relationships expressed above will be heavily relied onin mechanizing this desired result.

Before turning to a detailed description of the several embodiments ofthe present invention, it is necessary to describe briefly the variouslogic elements used in the block diagrams of FIGS. 4-7.

One of the most commonly used elements in these figures is anintegrator. Since the present invention is shown preferably in digitallogic form, the various integrators in FIGS. 4-7 will ordinarily bedigital integrators of any of several well known types. For this reason,the integrators in FIGS. 4-7 are shown by operational symbol only ratherthan by particular details of construction since the present inventionis not in any way limited to the particular construction of theintegrators used. FIG. 3 is a detailed illustration of the operationalsymbol for a digital integrator which will be referred to for anexplanation tents of the integrand register are repeatedly added to thecontents of the remainder register at a rate referred to as theiteration rate. Each time the remainder register overflows its capacity,there is an output from the integrator, generally in the form of adigital pulse. The frequency at which these pulses are generated is thetime integration of the number which is stored in the integrandregister. As is well known, if the number stored in the integrandregister is held constant, then the pulse output frequency will also beconstant and will be a function of the iteration rate and the numberstored in the integrand register. On the other hand, it is also known tovary the number in the integrand register so as to generate other thanlinear integrals.

The integrator symbol of FIG. 3 will be labeled throughout FIGS. 4-7with an indication of the number which is stored in the integrandregister. That is, for example, integrator 60 in FIG. 4 is labeledSpindle Speed so as to indicate that the number in the integrandregister is a function of the desired spindle speed. Similarly,integrator 62 in FIG. 4 is labeled with the number 1.9095" to indicatethat the number stored in the integrand register is held constant atthat value.

The pulse frequency which serves as the iteration rate for theintegrators is fed into the upper right-hand corner at the point labeledIteration Rate. A second input to the integrator of FIG. 3 is indicatedby the arrow at the bottom of the integrator. This particular input isused for supplying the integrator with so-called buffer" data. That is,as is well known in various types of control systems, the data input tothe system provides not only for active data being presently utilized bythe control system but also provides for buffer storage wherein futuredata is held until it is needed for the next sequence of operation.Therefore, the small rectangle on the bottom of the integrator symbol ofFIG. 3 is used to denote the input and location of the buffer data forthat particular function.

The lower right-hand corner of the integrator of FIG. 3 has two inputslabeled UP and DN." These two inputs are used to vary the number storedin the integrand register. That is, a pulse on the UP input results inincreasing the value of the number stored in the integrand register.Conversely, a pulse on the DN" input results in decreasing the value ofthe number stored in the integrand register. Generally, pulses at .theseinputs result in varying the value of the number stored in the integrandregister by one unit but it will be apparent that other variations arepossible. In this way, the value of the integrand can be varied duringoperation so as to generate something other than a straight linearoutput function.

The integrator of FIG. 3 has an additional output at the lefthand sidelabeled Monitor." This particular output is used to monitor the value ofthe number presently stored in the integrand register as will benecessary under various conditions of operation.

Finally, the output of the integrator of FIG. 3 emanates from theright-hand side and is, as described 'hereinbefore, a series of pulsesindicative of the integration which has taken place within theintegrator.

The logic symbol denoted by reference numeral 70 in FIG. 4 is a simpleNAND gate. The NAND gate 70 operates in the following fashion. When bothof its inputs are at logic I, the output (indicated by the circle) willbe a logic 0. Under all other conditions, the output of NAND gate 70will be logic 1.

Finally, the logic symbol denoted with the number 74 in FIG. 2 is asimple inverter which operates to invert the sense of the logic signalapplied at its input. That is, if the input is a logic 1 the output(indicated by the circle) will be a logic 0.

Conversely, if the input is a logic 0 the output will be an logic 1.

Turning now to FIG. 4, there is shown a block diagram illustrating thedetailed operation of a preferred embodiment of the present invention.Briefly stated, the embodiment of FIG. 4 mechanizes the relationshipsshown in equations (l)-(4) above.

Referring back to equation (4) above, it can be seen that integratingboth sides with respect to time yields:

T T J" =f 1.9095 SFM By separation' of terms Since the RPM term on theleft-hand side of equation (6) relates to the speed of the rotatingworkpiece, it can be appreciated that it may not be necessary tointegrate this term since it is already a pulse frequency and cantherefore be used as the iteration rate for integrating the radius termR.

Referring now to FIG. 4, it can be seen that the right-hand side of theequation (6) is mechanized by integrators 60, 62 whereas the left-handside of equation (6) is mechanized by integrator 64. That is, the outputof integrator 62 will be a pulse frequency proportional to theright-hand side of equation (6) whereas the pulse frequency output fromintegrator 64 will be proportional to the left-hand side of equation(6). In brief, it can be seen that the combination of integrators 60 and62 act as a first pulse generating means to generate a digital signalproportional to the desired SFM rate. Similarly, integrator 64 acts as asecond pulse generating means for generating a digital signalproportional to the product of the effective radius (R) of the rotatingworkpiece and the rotational speed (RPM) of the rotating workpiece.

This is accomplished in the following manner. The clock oscillator 41 ofFIG. 1 feeds to a frequency divider 66 whose output frequency isselected so as to generate the desired iteration rate for integrator 60.The data input to integrator 60 comes from the data input means 44 ofFIG. 1 and is the desired surface feet per minute (SFM) rate. Therefore,since the integrand of integrator 60 is the desired surface feet perminute, the output of integrator 60 is the time integral of the desiredsurface feet per minute as set forth in the right-hand side of equation(6). The output of the integrator 60 is used as the iteration rate forintegrator 62. The integrand register for integrator 62 is the constantfactor 1.9095. Therefore, it will be apparent that the output ofintegrator 62 is equal to the product of the two integrations set forthin the right-hand side of equation (6) above.

The input information for integrator 64 is nominally the effectiveradius of the workpiece 12. This information is initially supplied bythe data input means 44 of FIG. 1. It should be pointed out that theradius information need not necessarily be a precise definition of theactual radius of the workpiece. Instead, as used herein, the termeffective radius is defined as the distance (ordinarily in inches) fromthe center of the rotating workpiece to the present position of the tipof the cutting tool 24.

The iteration rate for the integrator 64 is supplied from a speedindicating means such as the digital encoder 68 which is mountedsomewhere in the spindle drive train so as to generate a digital signalwhich is proportional to the rotational speed of the spindle drive motor20 and therefore of the rotating workpiece 12. The pulse frequencyoutput from the encoder 68 is then fed to the iteration rate input ofintegrator 64 so as to mechanize the left-hand side of equation (6).

Referring back to FIG. 2, it will be remembered that the effectiveradius (which is the integrand of integrator 64) varies as the cuttingtool moves toward the center of the workpiece 12. This change inefi'ective radius is taken into account by varying the integrand ofintegrator 64. This is accomplished by the NAND gates 70, 72 andinverters 74, 76. As was pointed out in the description of the generalnumerical control system of FIG. 1, the arithmetic unit 42 generatespulses to the X" axis servo drive 46 and the Y" axis servo drive 48.Conventionally, each of these pulses indicates that the particular axisin question is to move a desired amount, say 0.000] inch. These pulsesare referred to as motion pulses. It will be apparent that with eachmotion pulse" the position of the cutting tool 24 will change. If thecutting tool is being commanded to move toward the center of therotating workpiece 12, it will also be apparent that the effectiveradius of the workpiece is decreasing and therefore that the integrandof integrator 64 must decrease. Conversely, if the cutting tool 24 isbeing commanded to move away from the center of the rotating workpiece12 (as, for example, at the completion of a cut) the effective radius ofthe workpiece 12 is increasing which requires an increase in the numberstored in the integrand register.

To accomplish these changes, the motion pulses to the X axis servo drive46 are fed to gates 70 and 72. For the purposes of the presentdiscussion, it will be assumed that these pulses go to logic 1 each timeit is desired to move the X axis a certain predetermined amount.

The other input to gate 70 is the signal XPOS. This signal is generatedelsewhere in the numerical control system and assumes the logic l statewhenever the X axis is commanded to move in the positive direction. Forthe sake of convention, it will be assumed that the positive directionof the X axis is toward the center of the rotating workpiece. Similarly,the signal XNEG forms the second input to gate 72. This signal will goto a logic 1 whenever the X axis is being commanded to move in thenegative direction (or away from the center of the rotating workpiece12).

When the X axis is commanded to move in the positive direction it willbe apparent that the cutting tool 24 is advanced toward the center ofthe workpiece thereby decreasing the effective radius of the workpiece12. In order to compensate for this in the radius integrator 64, it willbe necessary to decrease the integrand. This is accomplished byconnecting the output of gate 70 to the DN input of the integrator 64via inverter 74. Thus, when the X axis is being commanded to move in thepositive direction the signal XPOS will be a logic 1. With each logic 1pulse being fed to the X" axis servo drive 46, the output of gate 70will go to logic 0, causing the output of inverter 74 to go to logic 1.Since this output is con nected to the DN input of integrator 64, theintegrand register will be reduced a corresponding amount. Gate 72 andits associated inverter 76 act to increase the integrand when X" axis ismoving in the negative direction.

In order to fully mechanize the relationship of equation (6) above itwill be necessary to see that the pulse frequencies from integrators 62and 64 are maintained approximately the same so as to equalize the twosides of equation (6). Therefore, there must be provided comparisonmeans for comparing the output of these two integrators. In theembodiment of FIG. 4, the output pulse frequencies of integrators 62 and64 are compared by generating signals of varying phase and thencomparing the phase of the signals. It should be pointed out, however,that the present invention is not limited to comparing these outputsignals on a phase basis but rather encompasses any of several wellknown techniques of comparing two pulse frequencies.

In order to accomplish the desired phase comparison there is providedfirst and second phase varying digital counters such as the variablephase counters 78, 80. Each of these variable phase counters areconnected to the clock oscillator 41 via the trigger input terminal T soas to provide an input trigger signal which governs the basicfrequencies of these variable counters. In addition to the trigger inputterminal T, each of the variable phase counters 78, 80 has two auxiliaryinput terminals labeled ADV" and RET. These input terminals regulate thephase of the output signal from the variable phase counters. Pulses onthe ADV input cause the phase to advance a predetermined amount whereaspulses on the RET input cause the phase to retard a predeterminedamount. Variable phase counters of this general type are well known inthe art as shown, for example, in US. Pat. No. 3,258,667.

The output of the integrator 62 is connected to the ADV input of thevariable phase counter 78 and the output of integrator 64 is connectedto the ADV input of the variable phase counter 80. Each time a pulse isgenerated by integrator 62, the phase of the output of variable counter78 is advanced a predetermined amount. Similarly, each time a pulse isgenerated by integrator 64 the phase of the variable phase counter 80 isadvanced a similar amount. Therefore, it can be seen that the phase ofthe signals generated by the variable phase counters 78 and 80 areproportional to the pulse frequency signals output from integrators 62and 64, respectively. It will be apparent that the outputs ofintegrators 62, 64 could be connected to the RET inputs of counters 78,80 with the same net result.

The phase varying output signals from variable phase counter 78, 80 arethen fed to a phase comparator 82. The purpose of the phase comparator82 is to assure that the varia ble phase signals from counter 78, 80remain approximately equal. If these two signals are unequal, there willbe an output from the phase comparator 82 which will then be used toeither increase or decrease the spindle speed so as to equalize thesesignals. For this reason, the output of the phase comparator 82 isconnected to the input of a D/A converter 84. The output of D/Aconverter 84 will be an analog voltage signal proportional to the outputof the phase comparator 82. This signal is relayed to the spindle servodrive 50 of FIG. 1 which, in turn, controls the speed of the spindledrive motor 20. Since the encoder 68 is mechanically coupled to thespindle drive motor 20, it can be seen that the loop is now closed andthe relationship in equation (6) is fully mechanized.

It will be apparent to those skilled in the art that the variable phasesignals from counters 78, 80 will not be precisely in phase since somephase error will be required to supply power to the spindle drive motor20. However, for a constant spindle speed there will be a constant phasedifference so that the frequency of the signals from integrators 60, 62is equalized.

By way of brief explanation, consider the operation of the embodiment ofFIG. 4 as the cutting tool 24 is moved toward the center of the rotatingworkpiece 12. Since the integrands of integrators 60 and 62 remainconstant for a desired surface feet per minute characteristic, it willbe apparent that the output signal from integrator 62 is a pulse signalhaving a constant frequency. Similarly, the output of integrator 64 willhave a frequency which is proportional to the speed of the rotatingspindle and the initial effective radius of the workpiece 12. Assumingthat the initial spindle speed and the initial radius are properlyselected, it will be seen that the frequency of the pulse signal fromintegrator 64 will be equal to the frequency of the pulse signal fromthe integrator 62. In the alternative, it may be desirable to programthe numerical control system in such a way as to initially establish thespindle speed by programming the desired surface feet per minute and theeffective radius of the workpiece 12. After a predetermined time delay,the control system of FIG. 4 will have established the spindle speed atthe desired rate.

As soon as the cutting tool 24 begins to move toward the center of therotating workpiece 12, it will be apparent that the integrand of theradius integrator 64 decreases. If the frequency of the output fromencoder 68 (which establishes the iteration rate of integrator 64)remains the same, it will also be apparent that the output frequencyfrom the integrator 64 will accordingly decrease since its outputfrequency is a function of its iteration rate and the value of thenumber stored in its in its integrand register. When this happens, therewill be a phase dilference between the output of the variable phasecounters 78, 80 since the rate at which the phase of the output ofcounter 80 is advancing will be correspondingly decreased. This phasedifierence will cause a signal to be generated by phase comparator 82which is relayed via D/A converter 84 and the spindle servo drive 50 soas to cause the speed of the spindle drive motor 20 to increase. Thus,it can be seen that the embodiment of FIG. 4 operates to continuallyincrease the speed of the spindle drive motor (and therefore the therotational speed of the workpiece 12) as the effective radius of theworkpiece 12 decreases. In this way, the surface feet per minute is heldconstant.

After a out has been made in the workpiece 12, the cutting tool 24 willbe withdrawn from contact with the workpiece by programming the X axisto move away in the negative direction. When this happens, the effectiveradius of the workpiece 12 increases. In order to maintain the surfacefeet per minute characteristics, it will then be necessary to increasethe number in the radius integrator 64. This is accomplished by virtueof the fact that NAND gate 72 is connected to the UP input of theintegrator 64 so asto increase the value of the number stored in theintegrand as the cutting tool moves away from the workpiece 12.Therefore, it can also be seen that the embodiment of FIG. 4 allows theprogrammer to establish initial values of surface feet per minute andeffective radius. Thereafter he need only program the various motions ofthe cutting tool and the system of FIG. 4 will assure that the desiredsurface feet per minute characteristic is maintained for all cuts. If itbecomes desirable to change the surface feet per minute, this can bedone by simply programming a different value of surface feet per minutewithout having to affect the value of the radius. As describedhereinbefore, the spindle speed will be automatically adjusted toprovide the new surface feet per minute characteristics.

Turning now to FIG. 5, there is shown an alternative embodimentof thecontrol system disclosed in FIG. 4. In essence, the embodiment of FIG.'is identical to that of FIG. 4 with the exception that the means forcomparing the outputs of the integrators 62, 64 is changed. Therefore,to the extent that the system of FIG. 5 is similar to the system of FIG.4, it will be unnecessary to re-describe the operation. In addition,elements which are common to both FIGS. 4 and 5 bear the same referencenumerals.

Briefly, it will be recalled from the description of FIG. 4 that theintegrators 62 and 64 will each generate a series of pulses, thefrequency of which should be approximately equal. In the system of FIG.4, a pair of variable phase counters 78, 80 was used to generate phasevarying signals that were ultimately compared by the phase comparator82.

In the system of FIG. 5, there is provided a single variable phasecounter 90. As in the case of the variable phase counters of FIG. 4, theoutput of the clock oscillator 41 is fed to the trigger input terminal Tof the variable phase counter 90. However, the variable phase counter 90has the output of both integrators 62, 64 fed to its other inputs. Theoutput of the integrator 62 is fed to the ADV input so as to cause thephase of the variable phase counter 90 to advance a predetermined amounteach time a pulse is generated by integrator 62. Conversely, the outputof the integrator 64 is fed to the RET input of the variable phasecounter 90 so as to cause the variable phase counter 90 to retard apredetermined amount for each pulse from the integrator 64. It will beappreciated from a brief analysis of this circuit that the phase of thevariable phase counter 90 will be neither advanced nor retarded if thepulsefrequency from the two integrators 62, 64 is the same since theeffect of one will be cancelled by the effect of the other.

In addition to the variable phase counter 90, there is also provided afrequency divider 92. The frequency divider 92 has its input connectedto the clock oscillator 41. The division factor of the frequency divider92 is the same as the division factor of the variable phase counter 90.That is, the basic frequency of the output signal from the frequencydivider 92 is the same as the basic frequency of the output of counter90. Therefore, it can be appreciated that if the variable phase counter90 is neither advanced nor retarded in phase, The outputs of thevariable phase counter 90 and the frequency divider 92 will be the sameand will be in phase.

However, if the pulse frequency outputs from the integrators 62, 64 aredifierent, there will be a net difference and therefore the variablephase counter will be either advanced or retarded depending upon whichof the two frequencies is higher.

By way of illustration, suppose that the pulse frequency output from theintegrator 62 is-higher than the pulse frequency output from theintegrator 64. Under these circumstances it will be appreciated that itis necessary to increase the speed of the spindle drive motor 20 therebyincreasing the speed of the rotating workpiece 12 so as to achieve thedesired surface feet per minute characteristic. Under thesecircumstances, the phase of the variable phase counter 90 will beadvancing since the pulse frequency on the ADV input is higher than thepulse frequency on the RET input. This difference in phase is detectedby the phase comparator 82, relayed to the BIA converter 84, andultimately to the spindle servo drive 50 so as to increase the speed ofthe spindle drive motor 20 and thereby the rotational speed of theworkpiece 12. In this way, the desired surface feet per minutecharacteristic is re-established.

Turning now to FIG. 6, there is shown a still further embodiment of thecontrol system comprising the present invention. The embodiment of FIG.6 is the same as the embodiment of FIG. 4 with the exception of anadditional integrator 96 which acts as the speed indicating means forgenerating a digital signal proportional to the rotational speed of theworkpiece 12.

The integrator 96 will initially begin with a zero stored in itsintegrand register. The signal EOC is used for the iteration frequencyand is derived from the output of the frequency divider 66. In arecirculating storage system of the type described hereinbefore, thesignal EOC indicates the end of a complete circulation of data throughthe system. Thus, this signal indicates that the data has completelycirculated through the system once and is therefore the maximumiteration rate in that particular type of control system. It should bepointed out, however, that the iteration rate of the integrator 96 isnot critical. However, for maximum accuracy the iteration rate of theintegrator 96 should be set as high as possible.

The output of the encoder 68 is connected to the UP input of integrator96 so as to increase the number stored in the integrand register by oneeach time there is a pulse generated by the encoder 68. Conversely, theoutput of integrator 96 is connected to its own DN input. A briefanalysis of these connections will show that the integrand of theintegrator 96 will be increased with each pulse from the encoder 68 andcorrespondingly decreased by each pulse out of the integrator 96. If thespindle drive motor 20 (and therefore the workpiece 12) is rotating at aconstant speed it will be apparent that the number stored in theintegrand of integrator 96 will soon stabilized at a value necessary toequalize the pulse frequency outputs from the integrator 96 and theencoder 68. In this way, the output of the integrator 96 is exactly thesame as the output of the encoder 68 so that this output can be used asthe iteration rate for the integrator 64.

In addition, however, utilizing integrator 96 as the means forindicating the rotational speed of the workpiece provides an additionaladvantage in that the number stored in the integrand register isindicative of the actual spindle speed. As will be appreciated by thoseskilled in the art, there is often a need to provide a steady statedigital number indicative of the spindle speed. For this reason, thereis shown in FIG. 6 a spindle speed monitor 98 connected to the monitorinput of the integrator 96. The spindle speed monitor 98 may comprise,for example, a comparator of some type which analyzes the actual speedof the rotating spindle so as to recognize the need for the spindledrive system to change gears, etc.

Thus, it can be seen that the embodiment of FIG. 6 provides not only apulse frequency which is indicative of the speed of the rotatingworkpiece but also provides a steady state digital number stored in theintegrand of integrator 96 which is similarly indicative of the actualspindle speed. Thus, the integrator 96 acts as a digitizer which can beused in a variety of applications to provide an accurate digitalindication of the frequency of a pulse frequency signal.

It will be apparent that the embodiment of FIG. 6 can be furthermodified to include the means for comparing the output of integrators62, 64 as disclosed in the embodiment of FIG. 5.

Turning now to FIG. 7, there is shown a still further embodiment of thepresent invention which is in many respects identical to that shown inFIG. 4. To the extent that the system of FIG. 7 is identical with thatof FIG. 4, common reference numerals have been used and a detailedexplanation will not be given.

The primary difference between the system of FIG. 7 and that of thepreceding figures is that the pulse frequency signal for iterating theradius integrator 64 is not generated by the encoder 68 attached to thespindle drive motor 20. The system of FIG. 7 is particularly adapted tothose types of controlled machine tools whose spindle drive has anexcessively long time constant. That is, in certain types of machinetools the amount of time between a command to the spindle drive tochange speed and the actual change in the speed of the spindle may be solong as to cause significant instability in the control loop of thesystems of FIGS. 4-6. For this reason, the embodiment of FIG. 7generates a digital signal indicative of the commanded speed of thespindle rather than relying on the output of the encoder 68 to indicatethe actual speed of the spindle. In this way, the loop is closed but itis closed digitally through an additional integrator 100.

Integrator 100 is iterated at a relatively high frequency rate such asby the signal EOC generated by the frequency divider 66. The integrandregister of the integrator 100 is initially established at zero. The UPinput of the integrator 100 is connected by way of an exclusive ORcircuit 102 to the output of integrator 62. Similarly, the DN input ofthe integrator 100 is connected to the output of integrator 64 via theexclusive OR circuit 102. The exclusive OR circuit 102 includes a pairof input inverters 104, 106, a pair of gates 108, 110, and a pair ofoutput inverters 112, 114. An exclusive OR circuit of this type is wellknown in the art and requires no additional explanation except to pointout that the signal on output terminal Awill be a logic 1 if the logicsignal on input terminal A is a logic 1 and the logic signal on inputterminal 13 is a logic 0. Conversely, the signal on output terminal Bwill be a logic 1 if and only if the signal on output terminal B is alogic 1 and the signal on input terminal A is a logic 0.

As will be apparent to those skilled in the art, the purpose ofexclusive OR circuit 102 is to prevent pulses from arrivingsimultaneously at both the UP input and the DN input of integrator 100.

In operation, the integrand of integrator 100 will be increased eachtime there is an output pulse from the integrator 62 (unless this pulseis blocked by the exclusive OR circuit 102 due to a simultaneous pulseout of integrator 64). Conversely, the integrand of integrator 100 willbe decreased each time there is an output from integrator 64 (with thesame proviso as above).

Assume that the integrand of the integrator 100 is initially at zero andassume that a desired surface feet per minute has i been programmed intothe spindle speed integrator 60. Under these circumstances, integrator62 will begin to generate pulses at a frequency proportional to thedesired surface feet per minute characteristic. With each such pulse,the variable phase counter 78 will advance in phase, the phasedifference will be detected by phase comparator 82 and the speed of thespindle drive motor 20 will begin to increase. At the same time, thepulses from integrator 62 will be fed to the UP input of integrator 100so as to begin to increase the number in the integrand register toreflect the increase in the spindle speed. As the spindle speedincreases, however, the integrator 100 will begin to generate pulses asa result of increasing the number in its integrand register. Thesepulses will iterate the radius integrator 64 which will then begin togenerate pulses to advance the phase of the variable phase counter 80.Operation thus continues in this fashion until such time as the numberstored in the integrand of the integrator 100 is proportional to thecommanded speed of the spindle. At this point,

the outputs of the variable phase counters 78, 80 will be in phase withthe understanding that the integrand of the radius integrator 64 will becontinually changing if the X" axis is moving. Changes in the integrandof integrator 64 will continually change the commanded spindle speed inaccordance with the change in the effective radius of the workpiece 12.In this way, the spindle loop is efi'ectively closed digitally so as toovercome the deleterious effects of an excessively long time constantwithout sacrificing the capability to maintain a constant surface feetper minute characteristic.

An additional advantage of the circuit of FIG. 7 is that integrator 100has a number stored in its integrand which is proportional to the speedof the spindle. As in the embodiment of FIG. 6, therefore, this numbercan be fed to a spindle speed monitor circuit 116 so as to provide adigital number indicative of the present speed of the spindle for use inchanging gears, etc.

Finally, it will be apparent to those skilled in the art that the meansfor comparing the outputs of the integrators 62, 64 as disclosed in theembodiment of FIG. 5 could also be used in the embodiment of FIG. 7.

Although the present invention has been described with respect toseveral particular embodiments, the principles underlining thisinvention will suggest many additional modifications of these particularembodiments to those skilled in the art. Therefore, it is intended thatthe appended claims shall not be limited to the specific embodimentsshown, but rather shall cover all such modifications as fall within thetrue spirit and scope of the present invention.

What is claimed as new and desired to be secured by Letters Patent ofthe United States is: r

1. A digital control system for a numerically controlled machine toolfor maintaining a constant surface feet per unit time rate of metalremoval from a rotating workpiece by a moving cutting tool comprising:

a. a master clock oscillator for synchronizing the operation of thesystem;

b. data input means for indicating the effective radius of said rotatingworkpiece and the desired surface feet per unit time rate;

c. a first pulse generating means operatively connected to said datainput means for generating a first digital signal proportional to thedesired surface feet per unit time rate; first drive means forcontrollably moving the cutting tool relative to the rotational axis ofsaid rotating workpiece; e. second drive means for controllably rotatingsaid rotating workpiece;

f. speed indicating means for generating a digital signal proportionalto the rotational speed of said rotating workpiece;

g. a second pulse generating means operatively connected to said datainput means and to said speed indicating means for generating a seconddigital signal proportional to the product of the effective radius ofsaid rotating workpiece and the rotational speed of said rotatingworkpiece; and comparison means operatively connected to said first andsecond pulse generating means for comparing said first and seconddigital signals, the output of said comparison means being operativelyconnected to said second drive means so as to control the speed of saidrotating workpiece.

2. The digital control system recited in claim 1 wherein said data inputmeans also indicates the desired rate and direction of motion of saidcutting tool and further comprising motion command means operativelyconnected to said data input means for generating a digital signalproportional to said desired rate and direction of cutting tool motion,the output of said motion command means being operatively connected tosaid first drive means to control the operation thereof.

3. The digital control system recited in claim 2 wherein the output ofsaid motion command means is operatively connected to said second pulsegenerating means so as to continuously vary the effective radius of saidworkpiece in response to the commanded motion of said cutting tool.

4. The digital control system recited in claim 1 wherein said speedindicating means is operatively connected to said rotating workpiece soas to indicate the actual speed of said rotating workpiece.

5. The digital control system recited in claim 3 wherein said speedindicating means is operatively connected to said rotating workpiece soas to indicate the actual speed of said rotating workpiece.

6. The digital control system recited in claim 4 wherein saidspeed'indicating means comprises a digital encoder operatively connectedto said rotating workpiece.

7. The digital control system recited in claim 5 wherein said speedindicating means comprises a digital encoder operatively connected tosaid rotating workpiece.

8. The digital control system recited in claim 1 wherein said comparisonmeans includes first and second phase varying digital countersoperatively connected to said first and second pulse generating means,respectively, and to said master clock oscillator, said first and secondphase varying digital counters being operative to change phase apredetermined amount in response to pulses from said first and secondpulse generating means.

9. The digital control system recited in claim 3 wherein said outputsignal proportional to the phase difference between said outputs of saidfirst and second phase varying counters.

11. The digital control system recited in claim 9 wherein saidcomparisonmeans further comprises phase comparing means operativelyconnected to said first and second phase varying digital counters andbeing operative to generate an output signal proportional to the phasedifference between said outputs of said first and second phase varyingcounters.

12. The digital control system recited in claim 10 further comprising adigital-to-analog converter operatively connected to said phasecomparing means for generating an analog voltage output signalproportional to the output of said phase comparing means and a drivemotor operatively connected to the output of said digital-to-analogconverter.

13. The digital control system recited in claim 11 further comprising adigital-to-analog converter operatively connected to said phasecomparing means for generating an analog voltage output signalproportional to the output of said phase comparing means and a .drivemotor operatively connected to the output of said digital-to-analogconverter.

14. The digital control system recited in claim 1 wherein saidcomparison means includes first and second phase varying digitalcounters operatively connected to said first and second pulse generatingmeans, respectively, and to said master clock oscillator, said first andsecond phase varying means being operative to advance in phase apredetermined amount in response to pulses from said first and secondpulse generating means.

15. The digital control system recited in claim 3 wherein saidcomparison means includes first and second phase varying digitalcounters operatively connected to said first and second pulse generatingmeans, respectively, and to said master clock oscillator, said first andsecond phase varying means being operative to advance in phase apredetermined amount in response to pulses from said first and secondpulse generating means.

16. The digital control system recited in claim 1 wherein saidcomparison means includes a phase varying digital counter operativelyconnected to said first and second pulse generating means and to saidmaster clock oscillator and being operative to change phase in onedirection in response to pulses from said first pulse generating meansand to change phase in the opposite direction in response to pulses fromsaid second phase varying means. v

17. The digital control system recited in claim 3 wherein saidcomparison means includes a phase varying digital counter operativelyconnected to said first and second pulse generating means and to saidmaster clock oscillator and being operative to change phase in onedirection in response to pulses from said first pulse generating meansand to change phase in the opposite direction in response to pulses fromsaid second phase varying means.

18. The digital control system recited in claim 1 wherein said firstpulse generating means includes a first digital integrator including anintegrand register, said first digital integrator being operativelyconnected to said data input means whereby said data indicative of thedesired surface feet per unit time rate is stored in said integrandregister.

19. The digital control system recited in claim 3 wherein said firstpulse generating means includes a first digital integrator including anintegrand register, said first digital integrator being operativelyconnected to said data input means whereby said data indicative of thedesired surface feet per unit time rate is stored in said integrandregister.

20. The digital control system recited in claim 18 further comprising asecond integrator having a predetermined'constant number stored in theintegrand register and being operatively connected to the pulsefrequency output of said first integrator'whereby the output of saidfirst integrator acts as the iteration rate for said second integrator.

21. The digital control system recited in claim 19 further comprising asecond integrator having a predetermined constant number stored in theintegrand register and being operatively connected to the pulsefrequencyoutput of said first integrator whereby the output of said firstintegrator acts as the iteration rate for said second integrator.

22. The digital control system recited in claim 1 wherein said secondpulse generating means comprises a third digital integrator having theeffective radius of said rotating workpiece stored in the integrandregister thereof and having the output of saidspeed indicating means asthe iteration rate' for said third digital integrator.

23. The digital control system recited in claim 3 wherein said secondpulse generating means comprises a third digital integrator having theeffective radius of said rotating workpiece stored in the integrandregister thereof and having the output of said speed indicating means asthe iteration rate for said third digital integrator.

24. The digital control system recited in claim 23 wherein the output ofsaid motion command means is operatively connected to said integrandregister of said third integrator so as to increase the value of thenumber stored in said integrator when the output of said motion commandmeans calls for cutting tool motion in one direction and to decrease thevalue of the number stored in said integrand register when the output ofsaid motion command means calls for cutting tool motion in the oppositedirection.

25. The digital control system recited in claim 1 wherein said speedindicating means comprises a digital encoder operatively connected tosaid rotating workpiece and a fourth digital integrator operativelyconnected to said digital encoder whereby the output of said digitalencoder acts to increase the value of the number stored in the integrandregister of said fourth integrator, the pulse frequency output of saidfourth digital integrator being connected to said fourth digitalintegrator so as to decrease the value of the number stored in 1 saidintegrand register.

26. The digital control system recited in claim 3 wherein said speedindicating means comprises a digital encoder operatively connected tosaid rotating workpiece and a fourth digital integrator operativelyconnected to said digital encoder whereby the output of said digitalencoder acts to increase the value of the number stored in the integrandregister of said fourth integrator, the pulse frequency output of saidfourth 5 digital integrator being connected to said fourth digitalintegrator so as to decrease the value of the number stored in saidintegrand register.

27. The digital control system recited in claim 25 wherein said fourthdigital integrator is operatively connected to said master clockoscillator, the output of said master clock oscillator acting as theiteration rate of said fourth digital integrator.

28. The digital control system recited in claim 26 wherein said fourthdigital integrator is operatively connected to said master clockoscillator, the output of said master clock oscillator acting as theiteration rate of said fourth digital integrator.

29. The digital control system recited in claim 1 wherein said speedindicating means comprises a fifth digital integrator operativelyconnected to said first and second pulse generating means whereby pulsesfrom said first pulse generating means act to vary the value of thenumber stored in the integrand register of said fifth digital integratorin one direction and pulses from said second pulse generating means actto vary the value of the number stored in the integrand register of saidfifth digital integrator in the other direction.

30. The digital control system recited in claim 3 wherein said speedindicating means comprises a fifth digital integrator operativelyconnected to said first and second pulse generating means whereby pulsesfrom said first pulse generating means act to vary the value of thenumber stored in the integrand register of said fifth digital integratorin one direction and pulses from said second pulse generating means actto vary the value of the number stored in the integrand register of saidfifth digital integrator in the other direction.

31. The digital control system recited in claim 29 further comprisinggate means for operatively connecting said outputs of said first andsecond pulse generating means to said fifth digital integrator.

32. The digital control system recited in claim 30 further comprisinggate means for operatively connecting said outputs of said first andsecond pulse generating means to said fifth digital integrator.

33. The digital control system recited in claim 31 wherein said gatemeans comprises an exclusive OR gate so as to prevent pulses from bothof said first and said second pulse generating means from arrivingsimultaneously at said fifth digital integrator.

34. The digital control system recited in claim 32 wherein said gatemeans comprises an exclusive OR gate so as to prevent pulses from bothof said first and said second pulse generating means from arrivingsimultaneously at said fifth digital integrator.

35. A method of controlling a machine tool which is operable to removemetal from a rotating workpiece by a movable cutting tool comprising thesteps of:

a. generating a first digital signal proportional to a predetermineddesired rate of metal removal in terms of surface feet per unit time;

b. generating a second digital signal indicative of the effective radiusof said rotating workpiece;

c. generating a first pulse frequency signal proportional to said firstdigital signal; I

d. generating a second pulse frequency signal proportional to the speedof said rotating workpiece;

e. generating a third pulse frequency signal proportional to the productof said second digital signal and said second pulse frequency signal;

f. comparing said first and third pulse frequency signals so as togenerate an output signal proportional to the pulse frequency differencetherebetween; and

g. controlling the speed of said rotating workpiece in response to theoutput signal generated during said step of comparing.

36. The method recited in claim 35 comprising the additional steps of:

h. moving the cutting tool relative to the rotational axis of saidrotating workpiece;

i. generating a third digital signal indicative of the amount anddirection of movement of said cutting tool; and

j. varying the second digital signal in response to said third digitalsignal so as to continuously modify the effective radius of saidrotating workpiece.

37. The method recited in claim 35 wherein step (f) includes the stepsof;

l. generating a first phase varying signal whose phase is proportionalto the frequency of said first pulse frequency signal;

2. generating a second phase varying signal whose phase is proportionalto the frequency of said third pulse frequency signal;

3. comparing the phase of said first and second phase varying signals.

38. The method recited in claim 36 wherein step (f) includes the stepsof: I

l. generating a phase varying signal which varies in phase in onedirection at a rate proportional to the frequency of said first pulsefrequency signal and which varies in phase in one direction at a rateproportional to the frequency of said third pulse frequency signal;

2. generating a first constant frequency signal whose frequency is thesame as the basic frequency of said phase varying signal;

3. comparing the phase of said phase varying signal with the phase ofsaid first constant frequency signal.

39. The method recited in claim 36 wherein step (c) comprises the stepsof:

l. storing said first digital signal in the integrand register of afirst digital integrator; and s 2. iterating said digital integrator ata constant frequency rate whereby the output of said first digitalintegrator constitutes said first pulse frequency signal.

40. The method recited in claim 36 wherein step (e) comprises the stepsof:

l. storing said second digital signal in the integrand register of asecond digital integrator; and

2. iterating said second pulse frequency signal whereby the frequency ofsaid second pulse frequency signal whereby the output of said seconddigital integrator constitutes said third pulse frequency signal.

41. The method recited in claim 36 wherein step (c) comprises the stepsof:

l. storing said first digital signal in the integrand register of afirst digital integrator; and

2. iterating said second digital integrator at a constant frequency ratewhereby the output of said first digital integrator constitutes saidfirst pulse frequency signal; and

step (e) comprises the steps of:

l. storing said second digital signal in the integrand register of asecond digital integrator; and

2. iterating said second digital integrator at a rate determined by thefrequency of said second pulse frequency signal whereby the output ofsaid second digital integrator constitutes said third pulse frequencysignal.

42. The method recited in claim 36 wherein step (c) comprises the stepsof:

l. storing said first digital signal in the integrand register of afirst digital integrator;

2. iterating said first digital integrator at a constant frequency rate;

3. storing a fixed number in the integrand register of a third digitalintegrator; and

4. iterating said third digital integrator at a rate detennined by theoutput of said first digital integrator whereby the pulse frequencysignal.

43. The method recited in claim 36 wherein step (d) comprises the stepof rotating a digital encoder at a rate proportional to the speed ofsaid rotating workpiece so as to generate a pulse frequency digitalsignal whereby the output of said digital encoder constitutes saidsecond pulse frequency signal.

44. The method recited in claim 36 wherein step (d) comprises the stepsof:

1. rotating a digital encoder at a rate proportional to the speed ofsaid rotating workpiece so as to generate a pulse frequency outputsignal;

2. feeding the pulse frequency output signal from said digital encoderto a digital integrator so as to vary the number stored in the integrandregister in one direction; and

3. feeding the pulse frequency output signal from said digitalintegrator to said digital integrator so as to vary the number stored insaid integrand register in the opposite direction whereby the pulsefrequency output from said digital integrator constitutes said secondpulse frequency signal.

45. The method recited in claim 36 wherein step (d) comprises the stepsof:

l. rotating a digital encoder at a rate proportional to the speed ofsaid rotating workpiece so as to generate a pulse frequency digitalsignal;

2. feeding the pulse frequency signal from said digital encoder to adigital integrator so as to increase the number stored in the integrandregister thereof; and

3. feeding the pulse frequency output signal from said digitalintegrator to said digital integrator so' as to decrease the numberstored in said integrand register whereby the pulse frequency outputfrom said digital .integrator constitutes said second pulse frequencysignal.

46. The method recited in claim 36 wherein step (d) includes the stepsof:

l. feeding said first pulse frequency signal to a digital integrator soas to vary the number stored in the integrand register of said digitalintegrator in one direction;

2. feeding said third pulse frequency signal to said digital integratorso as to vary the number stored in said integrand register in the otherdirection; and

3. iterating said digital integrator at a predetermined rate whereby thepulse frequency output from said digital integrator constitutes saidsecond pulse frequency signal.

47. The method recited in claim 36 wherein step (d) includes the stepsof:

l. feeding said first pulse frequency signal to a digital integrator soas to increase the number stored in the integrand register of saiddigital integrator;

2. feeding said third pulse frequency signal to said digital integratorso as to decrease the number stored in said integrand register; and

3. iterating said digital integrator at a predetermined rate whereby thepulse frequency output from said digital integrator constitutes saidsecond pulse frequency signal.

1. A digital control system for a numerically controlled machine toolfor maintaining a constant surface feet per unit time rate of metalremoval from a rotating workpiece by a moving cutting tool comprising:a. a master clock oscillator for synchronizing the operation of thesystem; b. data input means for indicating the effective radius of saidrotating workpiece and the desired surface feet per unit time rate; c. afirst pulse generating means operatively connected to said data inputmeans for generating a first digital signal proportional to the desiredsurface feet per unit time rate; d. first drive means for controllablymoving the cutting tool relative to the rotational axis of said rotatingworkpiece; e. second drive means for controllably rotating said rotatingworkpiece; f. speed indicating means for generating a digital signalproportional to the rotational speed of said rotating workpiece; g. asecond pulse generating means operatively connected to said data inputmeans and to said speed indicating means for generating a second digitalsignal proportional to the product of the effective radius of saidrotating workpiece and the rotational speed of said rotating workpiece;and h. comparison means operatively connected to said first and secondpulse generating means for comparing said first and second digitalsignals, the output of said comparison means being operatively connectedto said second drive means so as to control the speed of said rotatingworkpiece.
 2. feeding said third pulse frequency signal to said digitalintegrator so as to decrease the number stored in said integrandregister; and
 2. generating a second phase varying signal whose phase isproportional to the frequency of said third pulse frequency signal; 2.generating a first constant frequency signal whose frequency is the sameas the basic frequency of said phase varying signal;
 2. iterating saiddigital integrator at a constant frequency rate whereby the output ofsaid first digital integrator constitutes said first pulse frequencysignal.
 2. iterating said second pulse frequency signal whereby thefrequency of said second pulse frequency signal whereby the output ofsaid second digital integrator constitutes said third pulse frequencysignal.
 2. iterating said first digital integrator at a constantfrequency rate;
 2. iterating said second digital integrator at aconstant frequency rate whereby the output of said first digitalintegrator constitutes said first pulse frequency signal; and step (e)comprises the steps of:
 2. iterating said second digital integrator at arate determined by the frequency of said second pulse frequency signalwhereby the output of said second digital integrator constitutes saidthird pulse frequency signal.
 2. feeding the pulse frequency outputsignal from said digital encoder to a digital integrator so as to varythe number stored in the integrand register in one direction; and 2.feeding the pulse frequency signal from said digital encoder to adigital integrator so as to increase the number stored in the integrandregister thereof; and
 2. feeding said third pulse frequency signal tosaid digital integrator so as to vary the number stored in saidintegrand register in the other direction; and
 2. The digital controlsystem recited in claim 1 wherein said data input means also indicatesthe desired rate and direction of motion of said cutting tool andfurther comprising motion command means operatively connected to saiddata input means for generating a digital signal proportional to saiddesired rate and direction of cutting tool motion, the output of saidmotion command means being operatively connected to said first drivemeans to control the operation thereof.
 3. The digital control systemrecited in claim 2 wherein the output of said motion command means isoperatively connected to said second pulse generating means so as tocontinuously vary the effective radius of said workpiece in response tothe commanded motion of said cutting tool.
 3. iterating said digitalintegrator at a predetermined rate whereby the pulse frequency outputfrom said digital integrator constitutes said second pulse frequencysignal.
 3. feeding the pulse frequency output signal from said digitalintegrator to said digital integrator so as to decrease the numberstored in said integrand register whereby the pulse frequency outputfrom said digital integrator constitutes said second pulse frequencysignal.
 3. feeding the pulse frequency output signal from said digitalintegrator to said digital integrator so as to vary the number stored insaid integrand register in the opposite direction whereby the pulsefrequency output from said digital integrator constitutes said secondpulse frequency signal.
 3. storing a fixed number in the integrandregister of a third digital integrator; and
 3. comparing the phase ofsaid phase varying signal with the phase of said first constantfrequency signal.
 3. comparing the phase of said first and second phasevarying signals.
 3. iterating said digital integrator at a predeterminedrate whereby the pulse frequency output from said digital integratorconstitutes said second pulse frequency signal.
 4. iterating said thirddigital integrator at a rate determined by the output of said firstdigital integrator whereby the output of said third digital integratorconstitutes said first pulse frequency signal.
 4. The digital controlsystem recited in claim 1 wherein said speed indicating means isoperatively connected to said rotating workpiece so as to indicate theactual speed of said rotating workpiece.
 5. The digital control systemrecited in claim 3 wherein said speed indicating means is operativelyconnected to said rotating workpiece so as to indicate the actual speedof said rotating workpiece.
 6. The digital control system recited inclaim 4 wherein said speed indicating means comprises a digital encoderoperatively connected to said rotating workpiece.
 7. The digital controlsystem recited in claim 5 wherein said speed indicating means comprisesa digital encoder operatively connected to said rotating workpiece. 8.The digital control system recited in claim 1 wherein said comparisonmeans includes first and second phase varying digital countersoperatively connected to said first and second pulse generating means,respectively, and to said master clock oscillator, said first and secondphase varying digital counters being operative to change phase apredetermined amount in response to pulses from said first and secondpulse generating means.
 9. The digital control system recited in claim 3wherein said comparison means includes first and second phase varyingdigital counters operatively connected to said first and second pulsegenerating means, respectively, and to said master clock oscillator,said first and second phase varying digital counters being operative tochange phase a predetermined amount in response to pulses from saidfirst and second pulse generating means.
 10. The digital control systemrecited in claim 8 wherein said comparison means further comprises phasecomparing means operatively connected to said first and second phasevarying digital counters and being operative to generate an outputsignal proportional to the phase difference between said outputs of saidfirst and second phase varying counters.
 11. The digital control systemrecited in claim 9 wherein said comparison means further comprises phasecomparing means operatively connected to said first and second phasevarying digital counters and being operative to generate an outputsignal proportional to the phase difference between said outputs of saidfirst and second phase varying counters.
 12. The digital control systemrecited in claim 10 further comprising a digital-to-analog converteroperatively connected to said phase comparing means for generating ananalog voltage output signal proportional to the output of said phasecomparing means and a drive motor operatively connected to the output ofsaid digital-to-analog converter.
 13. The digital control system recitedin claim 11 further comprising a digital-to-analog converter operativelyconnected to said phase comparing means for generating an analog voltageoutput signal proportional to the output of said phase comparing meansand a drive motor operatively connected to the output of saiddigital-to-analog converter.
 14. The digital control system recited inclaim 1 wherein said compArison means includes first and second phasevarying digital counters operatively connected to said first and secondpulse generating means, respectively, and to said master clockoscillator, said first and second phase varying means being operative toadvance in phase a predetermined amount in response to pulses from saidfirst and second pulse generating means.
 15. The digital control systemrecited in claim 3 wherein said comparison means includes first andsecond phase varying digital counters operatively connected to saidfirst and second pulse generating means, respectively, and to saidmaster clock oscillator, said first and second phase varying means beingoperative to advance in phase a predetermined amount in response topulses from said first and second pulse generating means.
 16. Thedigital control system recited in claim 1 wherein said comparison meansincludes a phase varying digital counter operatively connected to saidfirst and second pulse generating means and to said master clockoscillator and being operative to change phase in one direction inresponse to pulses from said first pulse generating means and to changephase in the opposite direction in response to pulses from said secondphase varying means.
 17. The digital control system recited in claim 3wherein said comparison means includes a phase varying digital counteroperatively connected to said first and second pulse generating meansand to said master clock oscillator and being operative to change phasein one direction in response to pulses from said first pulse generatingmeans and to change phase in the opposite direction in response topulses from said second phase varying means.
 18. The digital controlsystem recited in claim 1 wherein said first pulse generating meansincludes a first digital integrator including an integrand register,said first digital integrator being operatively connected to said datainput means whereby said data indicative of the desired surface feet perunit time rate is stored in said integrand register.
 19. The digitalcontrol system recited in claim 3 wherein said first pulse generatingmeans includes a first digital integrator including an integrandregister, said first digital integrator being operatively connected tosaid data input means whereby said data indicative of the desiredsurface feet per unit time rate is stored in said integrand register.20. The digital control system recited in claim 18 further comprising asecond integrator having a predetermined constant number stored in theintegrand register and being operatively connected to the pulsefrequency output of said first integrator whereby the output of saidfirst integrator acts as the iteration rate for said second integrator.21. The digital control system recited in claim 19 further comprising asecond integrator having a predetermined constant number stored in theintegrand register and being operatively connected to the pulsefrequency output of said first integrator whereby the output of saidfirst integrator acts as the iteration rate for said second integrator.22. The digital control system recited in claim 1 wherein said secondpulse generating means comprises a third digital integrator having theeffective radius of said rotating workpiece stored in the integrandregister thereof and having the output of said speed indicating means asthe iteration rate for said third digital integrator.
 23. The digitalcontrol system recited in claim 3 wherein said second pulse generatingmeans comprises a third digital integrator having the effective radiusof said rotating workpiece stored in the integrand register thereof andhaving the output of said speed indicating means as the iteration ratefor said third digital integrator.
 24. The digital control systemrecited in claim 23 wherein the output of said motion command means isoperatively connected to said integrand register of said thirdintegrator so as to increase the value of the number stored in saidintegrator when the outPut of said motion command means calls forcutting tool motion in one direction and to decrease the value of thenumber stored in said integrand register when the output of said motioncommand means calls for cutting tool motion in the opposite direction.25. The digital control system recited in claim 1 wherein said speedindicating means comprises a digital encoder operatively connected tosaid rotating workpiece and a fourth digital integrator operativelyconnected to said digital encoder whereby the output of said digitalencoder acts to increase the value of the number stored in the integrandregister of said fourth integrator, the pulse frequency output of saidfourth digital integrator being connected to said fourth digitalintegrator so as to decrease the value of the number stored in saidintegrand register.
 26. The digital control system recited in claim 3wherein said speed indicating means comprises a digital encoderoperatively connected to said rotating workpiece and a fourth digitalintegrator operatively connected to said digital encoder whereby theoutput of said digital encoder acts to increase the value of the numberstored in the integrand register of said fourth integrator, the pulsefrequency output of said fourth digital integrator being connected tosaid fourth digital integrator so as to decrease the value of the numberstored in said integrand register.
 27. The digital control systemrecited in claim 25 wherein said fourth digital integrator isoperatively connected to said master clock oscillator, the output ofsaid master clock oscillator acting as the iteration rate of said fourthdigital integrator.
 28. The digital control system recited in claim 26wherein said fourth digital integrator is operatively connected to saidmaster clock oscillator, the output of said master clock oscillatoracting as the iteration rate of said fourth digital integrator.
 29. Thedigital control system recited in claim 1 wherein said speed indicatingmeans comprises a fifth digital integrator operatively connected to saidfirst and second pulse generating means whereby pulses from said firstpulse generating means act to vary the value of the number stored in theintegrand register of said fifth digital integrator in one direction andpulses from said second pulse generating means act to vary the value ofthe number stored in the integrand register of said fifth digitalintegrator in the other direction.
 30. The digital control systemrecited in claim 3 wherein said speed indicating means comprises a fifthdigital integrator operatively connected to said first and second pulsegenerating means whereby pulses from said first pulse generating meansact to vary the value of the number stored in the integrand register ofsaid fifth digital integrator in one direction and pulses from saidsecond pulse generating means act to vary the value of the number storedin the integrand register of said fifth digital integrator in the otherdirection.
 31. The digital control system recited in claim 29 furthercomprising gate means for operatively connecting said outputs of saidfirst and second pulse generating means to said fifth digitalintegrator.
 32. The digital control system recited in claim 30 furthercomprising gate means for operatively connecting said outputs of saidfirst and second pulse generating means to said fifth digitalintegrator.
 33. The digital control system recited in claim 31 whereinsaid gate means comprises an exclusive OR gate so as to prevent pulsesfrom both of said first and said second pulse generating means fromarriving simultaneously at said fifth digital integrator.
 34. Thedigital control system recited in claim 32 wherein said gate meanscomprises an exclusive OR gate so as to prevent pulses from both of saidfirst and said second pulse generating means from arrivingsimultaneously at said fifth digital integrator.
 35. A method ofcontrolling a machine tool which is operable to remove metal from arotating worKpiece by a movable cutting tool comprising the steps of: a.generating a first digital signal proportional to a predetermineddesired rate of metal removal in terms of surface feet per unit time; b.generating a second digital signal indicative of the effective radius ofsaid rotating workpiece; c. generating a first pulse frequency signalproportional to said first digital signal; d. generating a second pulsefrequency signal proportional to the speed of said rotating workpiece;e. generating a third pulse frequency signal proportional to the productof said second digital signal and said second pulse frequency signal; f.comparing said first and third pulse frequency signals so as to generatean output signal proportional to the pulse frequency differencetherebetween; and g. controlling the speed of said rotating workpiece inresponse to the output signal generated during said step of comparing.36. The method recited in claim 35 comprising the additional steps of:h. moving the cutting tool relative to the rotational axis of saidrotating workpiece; i. generating a third digital signal indicative ofthe amount and direction of movement of said cutting tool; and j.varying the second digital signal in response to said third digitalsignal so as to continuously modify the effective radius of saidrotating workpiece.
 37. The method recited in claim 35 wherein step (f)includes the steps of;
 38. The method recited in claim 36 wherein step(f) includes the steps of:
 39. The method recited in claim 36 whereinstep (c) comprises the steps of:
 40. The method recited in claim 36wherein step (e) comprises the steps of:
 41. The method recited in claim36 wherein step (c) comprises the steps of:
 42. The method recited inclaim 36 wherein step (c) comprises the steps of:
 43. The method recitedin claim 36 wherein step (d) comprises the step of rotating a digitalencoder at a rate proportional to the speed of said rotating workpieceso as to generate a pulse frequency digital signal whereby the output ofsaid digital encoder constitutes said second pulse frequency signal. 44.The method recited in claim 36 wherein step (d) comprises the steps of:45. The method recited in claim 36 wherein step (d) comprises the stepsof:
 46. The method recited in claim 36 wherein step (d) includes thesteps of:
 47. The method recited in claim 36 wherein step (d) includesthe steps of: